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Simplifying 27x2 + -63.75x + 28.875 = 0 Reorder the terms: 28.875 + -63.75x + 27x2 = 0 Solving 28.875 + -63.75x + 27x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. 1.069444444 + -2.361111111x + x2 = 0 Move the constant term to the right: Add '-1.069444444' to each side of the equation. 1.069444444 + -2.361111111x + -1.069444444 + x2 = 0 + -1.069444444 Reorder the terms: 1.069444444 + -1.069444444 + -2.361111111x + x2 = 0 + -1.069444444 Combine like terms: 1.069444444 + -1.069444444 = 0.000000000 0.000000000 + -2.361111111x + x2 = 0 + -1.069444444 -2.361111111x + x2 = 0 + -1.069444444 Combine like terms: 0 + -1.069444444 = -1.069444444 -2.361111111x + x2 = -1.069444444 The x term is -2.361111111x. Take half its coefficient (-1.180555556). Square it (1.393711421) and add it to both sides. Add '1.393711421' to each side of the equation. -2.361111111x + 1.393711421 + x2 = -1.069444444 + 1.393711421 Reorder the terms: 1.393711421 + -2.361111111x + x2 = -1.069444444 + 1.393711421 Combine like terms: -1.069444444 + 1.393711421 = 0.324266977 1.393711421 + -2.361111111x + x2 = 0.324266977 Factor a perfect square on the left side: (x + -1.180555556)(x + -1.180555556) = 0.324266977 Calculate the square root of the right side: 0.569444446 Break this problem into two subproblems by setting (x + -1.180555556) equal to 0.569444446 and -0.569444446.Subproblem 1
x + -1.180555556 = 0.569444446 Simplifying x + -1.180555556 = 0.569444446 Reorder the terms: -1.180555556 + x = 0.569444446 Solving -1.180555556 + x = 0.569444446 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.180555556' to each side of the equation. -1.180555556 + 1.180555556 + x = 0.569444446 + 1.180555556 Combine like terms: -1.180555556 + 1.180555556 = 0.000000000 0.000000000 + x = 0.569444446 + 1.180555556 x = 0.569444446 + 1.180555556 Combine like terms: 0.569444446 + 1.180555556 = 1.750000002 x = 1.750000002 Simplifying x = 1.750000002Subproblem 2
x + -1.180555556 = -0.569444446 Simplifying x + -1.180555556 = -0.569444446 Reorder the terms: -1.180555556 + x = -0.569444446 Solving -1.180555556 + x = -0.569444446 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.180555556' to each side of the equation. -1.180555556 + 1.180555556 + x = -0.569444446 + 1.180555556 Combine like terms: -1.180555556 + 1.180555556 = 0.000000000 0.000000000 + x = -0.569444446 + 1.180555556 x = -0.569444446 + 1.180555556 Combine like terms: -0.569444446 + 1.180555556 = 0.61111111 x = 0.61111111 Simplifying x = 0.61111111Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.750000002, 0.61111111}
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